Question 15

3 3 3 13. If x represents the mean of n observations x1, x2, ..., xn, then value of ( xi − x ) is: i =1

• (A)–1
• (B)0
• (C)1
• (D)n – 1 14. If each observation of the data is increased by 5, then their mean (A) remains the same (B) becomes 5 times the original mean (C) is decreased by 5 (D) is increased by 5 15. Let x be the mean of x1, x2, ... , xn and y the mean of y1, y2, ... , yn. If z is the mean of x1, x2, ... , xn, y1, y2, ... , yn, then z is equal to x+y x+y x+y (A) x+y (B) (C) (D) 2 n 2n 16. If x is the mean of x1, x2, ... , xn, then for a ≠ 0, the mean of ax1, ax2, ..., axn, x1 , x2 , ... , xn is a a 1 1 1 x 1 x a + x (A) a + x (B) a + (C) a + (D) a a a 2 a n 2n 17. If x1 , x2 , x3 , ... , xn are the means of n groups with n1, n2, ... , nn number of observations respectively, then the mean x of all the groups taken together is given by : n n n n ni xi ni xi ni xi (A) ni xi (B) i =1 n2 (C) i =1 (D) i =1 2n i =1 ni i =1 18. The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be : (A) 50.5 (B) 51 (C) 51.5 (D) 52 19. There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be –3.5. The mean of the given numbers is : (A) 46.5 (B) 49.5 (C) 53.5 (D) 56.5 20. The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is : (A) 23 (B) 36 (C) 38 (D) 40 21. The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is (A) 45 (B) 49.5 (C) 54 (D) 56 22. For drawing a frequency polygon of a continous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abcissae are respectively : (A) upper limits of the classes (B) lower limits of the classes (C) class marks of the classes (D) upper limits of perceeding classes 23. Median of the following numbers : 4, 4, 5, 7, 6, 7, 7, 12, 3 is (A) 4 (B) 5 (C) 6 (D) 7 24. Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is (A) 14 (B) 15 (C) 16 (D) 17 25. In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is : (A) 0.5 (B) 0.6 (C) 0.7 (D) 0.8 STATISTICS AND PROBABILITY 135 26. In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is : (A) 0.25 (B) 0.50 (C) 0.75 (D) 0.80 27. In a medical examination of students of a class, the following blood groups are recorded: Blood group A AB B O Number of students 10 13 12 5 A student is selected at random from the class. The probability that he/she has blood group B, is :